Distribution simply means the right to distribute (and make money from) any release that they are given - the actual footage for the release (with the exception of some commentary/special features) is complete before they get their hands on it. That puts the OUT in Disney's hands to restore, and simply means that they are forced to deliver the finished product to be released through Fox.
Ultimately, I would assume this sets fan projects up to be targeted from two different directions - illegal distribution (which fanedits are not... but who knows how they'll view that) effects both companies equally, and it is in the interests of both Fox and Disney to protect their assets.
However, it is my belief that fan projects help rather than hinder, and the business savvy people at these companies probably know this. Sure, Disney sued some daycare for painting Disney characters on the wall, but that is well within their rights when they sell wallpaper and posters and wall decals. They could never sell edits, and as such aren't missing out on profits from this particular area of fandom.